A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Page xxi
... tangent 332 215. Modification of the equation in case the function is ( a ) implicit , ( 8 ) homogeneous ... 333 216. Equation to the tangent , when the equation to the curve is homogeneous and of three variables 334 217. Equation to ...
... tangent 332 215. Modification of the equation in case the function is ( a ) implicit , ( 8 ) homogeneous ... 333 216. Equation to the tangent , when the equation to the curve is homogeneous and of three variables 334 217. Equation to ...
Page xxiii
... Tangents and normals to polar curves . 269. The values of ds , and of lines and quantities connected with the tangent and the normal 415 270. Other values of p 417 271. The same quantities in terms of p and r 417 272. Examples in ...
... Tangents and normals to polar curves . 269. The values of ds , and of lines and quantities connected with the tangent and the normal 415 270. Other values of p 417 271. The same quantities in terms of p and r 417 272. Examples in ...
Page xxvi
... tangent plane to a curved surface .. 333. The direction - cosines of the tangent - plane 498 500 501 334 , 335. Modified forms of the equation to the tangent plane , when the equation to the surface is ( a ) explicit , ( B ) homo ...
... tangent plane to a curved surface .. 333. The direction - cosines of the tangent - plane 498 500 501 334 , 335. Modified forms of the equation to the tangent plane , when the equation to the surface is ( a ) explicit , ( B ) homo ...
Page 30
... tangent at any point is the line which coincides with the straight line joining the point and its consecutive point ; that is , the tangent is the element produced . In elementary treatises on conics , the tan- gent to a conic is ...
... tangent at any point is the line which coincides with the straight line joining the point and its consecutive point ; that is , the tangent is the element produced . In elementary treatises on conics , the tan- gent to a conic is ...
Page 37
... tangent and PM the sine of the arc . At p draw a tangent to the circle , viz . PT ' , and draw the other lines as in the figure ; then , since TPT is a right angle , TT ' is greater than PT , . ' . AT > AT + T'P ; and because two sides ...
... tangent and PM the sine of the arc . At p draw a tangent to the circle , viz . PT ' , and draw the other lines as in the figure ; then , since TPT is a right angle , TT ' is greater than PT , . ' . AT > AT + T'P ; and because two sides ...
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Common terms and phrases
a₁ algebraical ascending powers b₁ becomes calculated change of sign changes sign coefficients constant curve d²u d²x d²y d2y dx2 d³u d³y denominator determine differential equation dr dr dr dx dx dr dx dx dx dy dx dz dx² dx2 dy2 dy d2u dy dx dy dy dy dz dy² dy³ dz dx dz dz equal equicrescent Evaluate explicit function expression F(xo F(xo+h factor finite quantity fraction given Hence homogeneous function increases increments indeterminate form infinite infinitesimal Infinitesimal Calculus infinity logarithm loge maxima and minima minimum value negative partial derived-functions particular values positive primitive equation proper fraction replaced result roots Similarly sin x singular value substituting suppose symbols Taylor's Series tion total differentials vanish variation whence x+▲x zero
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